Publications

• Refereed Journal Publications
  
  
  • 26) J. Jang, F. Li, J.-M. Qiu, T. Xiong, High Order Asymptotic Preserving DG-IMEX Schemes for Discrete-Velocity Kinetic Equations in a Diffusive Scaling, arxiv:1306.0227, submitted, 2013
  
  
  • 25) H. Yang and F. Li, Error Estimates of Runge-Kutta Discontinuous Galerkin Methods for the Vlasov-Maxwell System, arXiv:1306.0636, submitted, 2013
  
  
  • 24) Y(ingda). Cheng, I. Gamba, F. Li, and P. Morrison, Discontinuous Galerkin Methods for Vlasov-Maxwell Equations, arxiv:1302.2136, submitted, 2013
  
  
  • 23) M. Li, P. Guyenne, F. Li, and L. Xu, High order well-balanced CDG-FE methods for shallow water waves by a Green-Naghdi model, submitted, 2012
  
  
  • 22) J. Gopalakrishnan, F. Li, N.-C. Nguyen, and J. Peraire, Spectral approximations by the HDG method, submitted, 2012
  
  
  • 21) H. Yang, F. Li, and J. Qiu, Dispersion and dissipation errors of two fully discrete discontinuous Galerkin methods, [PDF], Journal of Scientific Computing, DOI: 10.1007/s10915-012-9647-y, v55 (2013), pp.552-574
  
  
  • 20) Y(ue). Cheng, F. Li, J. Qiu, and L. Xu, Positivity-preserving DG and central DG methods for ideal MHD equations, [PDF], Journal of Computational Physics, DOI: 10.1016/j.jcp.2012.12.019, v238 (2013), pp.255-280
  
  
  • 19) S. Yakovlev, L. Xu, and F. Li, Locally divergence-free central discontinuous Galerkin methods for ideal MHD equations, [PDF], Journal of Computational Science, DOI: 10.1016/j.jocs.2012.05.002, v4 (2013), pp.80-91. (Special issue on Computational Methods for Hyperbolic Problems)
  
  
  • 18) F. Li and L. Xu, Arbitrary order exactly divergence-free central discontinuous Galerkin methods for ideal MHD equations, [PDF], Journal of Computational Physics, DOI: 10.1016/j.jcp.2011.12.016, v231 (2012), pp.2655-2675
  
  
  • 17) F. Li, On the negative-order norm accuracy of a local-structure-preserving LDG method, [PDF], Journal of Scientific Computing, DOI: 10.1007/s10915-011-9503-5, v51 (2012), pp.213-223
  
  
  • 16) F. Li, L. Xu and S. Yakovlev, Central discontinuous Galerkin methods for ideal MHD equations with the exactly divergence-free magnetic field, [PDF], Journal of Computational Physics, DOI:10.1016/j.jcp.2011.03.006, v230 (2011), pp.4828-4847. (Correction: in section 4.2.6, it is `with the darker area representing the smaller value)
  
  
  • 15) W. Guo, F. Li and J. Qiu, Local-structure-preserving discontinuous Galerkin methods with Lax-Wendroff type time discretizations for Hamilton-Jacobi equations, [PDF], Journal of Scientific Computing, DOI: 10.1007/s10915-010-9434-6, v47 (2011), pp.239-257
  
  
  • 14) Y.-T. Zhang, S. Chen, F. Li, H.-K. Zhao and C.-W. Shu, Uniformly accurate discontinuous Galerkin fast sweeping methods for Eikonal equations, [PDF], SIAM Journal on Scientific Computing, DOI: 10.1137/090770291, v33 (2011), pp.1873-1896
  
  
  • 13) B. Cockburn, J. Gopalakrishnan, F. Li, N.-C. Nguyen, and J. Peraire, Hybridization and postprocessing techniques for mixed eigenfunctions, [PDF] , SIAM Journal on Numerical Analysis, DOI: 10.1137/090765894, v48 (2010), pp.857-881
  
  
  • 12) F. Li and S. Yakovlev, A central discontinuous Galerkin method for Hamilton-Jacobi equations, [PDF], Journal of Scientific Computing, DOI: 10.1007/s10915-009-9340-y, v45 (2010), pp.404-428. (Special issue in memory of Professor David Gottlieb)
  
  
  • 11) S. C. Brenner, F. Li and L.-Y. Sung, Nonconforming Maxwell eigensolvers, [PDF], Journal of Scientific Computing, v40 (2009), pp.51-85
  
  
  • 10) S. C. Brenner, F. Li and L.-Y. Sung, A nonconforming penalty method for a two-dimensional curl-curl problem, [PDF], Mathematical Models and Methods in Applied Mathematics, v19 (2009), pp.651-668
  
  
  • 9) F. Li, C.-W. Shu, Y.-T. Zhang and H.-K. Zhao, A second order DGM based fast sweeping method for Eikonal equations, [PDF] Journal of Computational Physics, DOI: 10.1016/j.jcp.2008.05.018, v227 (2008), pp.8191-8208
  
  
  • 8) S. C. Brenner, J. Cui, F. Li and L.-Y. Sung, A nonconforming finite element method for a two-dimensional curl-curl and grad-div problem, [PDF]  Numerische Mathematik, v109 (2008), pp.509-533
  
  
  • 7) S. C. Brenner, F. Li and L.-Y. Sung, A locally divergence-free interior penalty method for two-dimensional curl-curl problems, [PDF]  SIAM Journal on Numerical Analysis, v46 (2008), pp.1190-1211
  
  
  • 6) S. C. Brenner, F. Li and L.-Y. Sung, A locally divergence-free nonconforming finite element method for the reduced time-harmonic Maxwell equations, [PDF]  Mathematics of Computation, v76 (2007), pp.573-595
  
  
  • 5) F. Li and C.-W. Shu, A local-structure-preserving local discontinuous Galerkin method for the Laplace equation, [PDF]  [Some Correction] Methods and Applications of Analysis, v13 (2006), pp.215-233 (Special issue dedicated to Professor Bjorn Engquist on the occasion of his 60th birthday)
  
  
  • 4) F. Li and C.-W. Shu, Reinterpretation and simplified implementation of a discontinuous Galerkin method for Hamilton-Jacobi equations, [Abstract]  [PDF]  Applied Mathematics Letters, v18 (2005), pp.1204-1209
  
  
  • 3) F. Li and C.-W. Shu, Locally divergence-free discontinuous Galerkin methods for MHD equations, [Abstract]  [PDF]  Journal of Scientific Computing, v22-23 (2005), pp.413-442
  
  
  • 2) B. Cockburn, F. Li and C.-W. Shu, Locally divergence-free discontinuous Galerkin methods for the Maxwell equations, [Abstract]  [PDF]  Journal of Computational Physics, v194 (2004), pp.588-610
  
  
  • 1) L.-A. Ying and F. Li, Exterior Problem of the Darwin Model and its Numerical Computation, [Abstract]  [PDF]  Mathematical Modelling and Numerical Analysis, v37 (2003), pp.515-532
  
  
• Publications in Conference and Workshop Proceedings
  
  
  • 4) S. C. Brenner, F. Li and L.-Y. Sung, Nonconforming Maxwell eigensolvers, Oberwolfach Report No. 36, 2008, the proceedings for the workshop "Nonstandard Finite Element Methods, Mathematisches Forschungsinstitut Oberwolfach, Germany, August 10-16, 2008, pp.42-43
  
  
  • 3) F. Li, C.-W. Shu, Y.-T. Zhang and H.-K. Zhao, A DGM-based fast sweeping method for Eikonal equations, Oberwolfach Report No. 36, 2008, the proceedings for the workshop "Nonstandard Finite Element Methods", Mathematisches Forschungsinstitut Oberwolfach, Germany, August 10-16, 2008, pp. 38
  
  
  • 2) S. C. Brenner, F. Li and L.-Y. Sung, A locally divergence-free nonconforming finite element method for the reduced time-harmonic Maxwell equations, [PDF]  Proceedings of the joint Workshop by AWM and MSRI: The Legacy of Ladyzhenskaya and Oleinik, 2006, pp.187-191
  
  
  • 1) B. Cockburn, F. Li and C.-W. Shu, Discontinuous Galerkin methods for equations with divergence-free solutions: preliminary results, the proceedings of the Second MIT Conference on Computational Fluid and Solid Mechanics, K.J. Bathe, Editor, June 2003, Elsevier Science, pp.1900-1902
  
  
• Unpublished
  
  
  • F. Li, A priori error estimates of a local-structure-preserving LDG method, [PDF], May 2011